Since the derivative is bounded, using the mean value theorem you get that the function is uniformly continous.

The only thing is that this requires him to assume is differentiable and furthermore that it's derivative is . (If they haven't proved that is continuous yet, it's unlikely they've proved its derivative is .)

The only thing is that this requires him to assume is differentiable and furthermore that it's derivative is . (If they haven't proved that is continuous yet, it's unlikely they've proved its derivative is .)